Buster is an informal word for mister. "Make with the" means bring, make it happen, serve.
Make with the music-play some music
Make with the money-give me the money (that you owe me)
Make with the excuses-explain to me why you failed at something
So "Make with the beers, buster!" means "Give us/serve us beer, mister ! right away."

Example sentences using "Buster"

"Ball buster", as far as I know, refers to people who are dominant and aggressive. This is a slang word though.
Usually it is used for women, who emasculate men (if taken literally, they shatter their balls!!), or who challenge male dominance in different fields; they are supposed to be relentlessly aggressive against men and are able to overpower them with their intelligence and verbal prowess! This word usually carries negative connotations and is used informally.
E.g.,
1. "My boss is such a ball buster, she always overworks her subordinates."
2. "I wanted to ask that girl out. I was really well mannered, respectful, and treated her as a lady. But, she on the other hand, made it a point to show off that she has higher salary than me. I even opened the door for her, and she slammed the door in my face.. Geez, she's such a ball buster."
I'm sorry for the long last example! But I thought it's better to explain her behavior with examples, to describe the meaning of the word!
I hope this is helpful :)

‎I watched Alien 3 today. It is one of my favorite movies. Many people say Alien 3 is the worst fucking movie in Alien franchise. Stop talking shit.
Alien 3 is the most beautiful of them all. Reading a sacred textbook during funeral in blast furnace while describing the birth of dog(ox) xenomorph at the same time. Death versus birth, this is art itself!!
Especially when Ripley holds the queen chest buster within her chest jumping to death in the blast furnance...what a beautiful death scene! Ripley lost her real daughter, and her friend close to real daughter. But in the end she lost her enemy as if she was her daughter because "she" was born from her body! She finally could die as a mother, right ?!!!! Why should this movie be lined up with shit movies?!
! are as optional in English as they are in Japanese. No spaces between additional ! or ?.
Your statement would be very inpolite in a classroom, but sounds natural with friends.
Good taste in movies.